Compaction Model

The compaction of the sediments is controlled by the impact of effective stress on the slow viscous flow of the rock, during geologic time. The volume change of the solid rock is assumed to be negligible, compared to the bulk volume change.

Lithologies are defined by their mineral composition. The model has 10 pre-defined lithologies, 6 sedimentary rocks (sandstone, shale, clay, limestone, dolomite, and lignite), 2 evaporites (halite and anhydrite), and 2 igneous rock types (granite and basalt) all defined by their mineral composition. The pre-defined minerals include 9 inorganic minerals (quartz, feldspar, illite, smectite, kaolinite, calcite, dolomite, halite, anhydrite, lignite) and 15 organic minerals (humic acid, fulvic acid, amino acid, uric acid, coke, graphite, C vitrinite, humin, phenol, lignin, cholesterol, lipid, protein, carbohydrate, pre-coke ). The user can optionally add new sediments or minerals. The mineral composition is used when the physical properties such as solid density, heat capacity, and thermal conductivity of the lithologies are calculated. The viscous drag of the sediment can be calculated from its mineral composition and the texture data of the minerals or directly by setting the texture data of the sediment.

The conservation of mass for the minerals is given by a set of time-space partial differential equation, which also accounts for reaction of minerals.

The compaction of the sediments is controlled by the impact of effective stress on the slow viscous deformation of the rock. The implementation considers two domains within the solid mineral. One domain which is in equilibrium and another which is deforming due to the pressure differential between the internal rock stress and the contacting fluid pressure. The deformation changes the curved mineral surface to a more plane surface allowing the minerals to compact and reduce the porosity. The mineral geometry is represented by an equivalent sphere, which dynamically will grow in size by rearranging mineral volume lost at caps, created by the viscous deformation. The underlying assumption is that the mineral volume is preserved and the mineral density is constant.

The over burden is assumed to be in equilibrium with the rock stress, and the fluid pressure.

This rock movements are solved in 1D, meaning that rock phase is only allowed to move in the vertical direction. The system of equations are however formulated is such a way that the extension to 3D movements should be straight forward.

The viscous deformation of the mineral molecules is caused by the localized strain trying to equilibrate itself. Therefore the mineral viscosity is quantified by the product of shear modulus, G, and the time between two dislocations. The dislocation time is quantified using an Arrhenius type reaction rate, and equating it to the reciprocal of the reaction rate. The activation energy and the pre-exponential factor are rarely reported in literature. Here the parameters are derived using Wood's compensation law and a zero-dependence reference viscosity of 10^20 pas and a reference shear modulus of 10^9 pa.

The model also provides an option to use empirical compaction curves instead of the conservation of momentum for the solid phase. The compaction curves are bases on Terzaghi's (1925) idea, that the change in porosity is assumed to be a direct response to the change in effective stress. During loading an exponential empirical relation is describing the porosity-effective stress relation. During unloading the empirical relation is corrected for the compaction being irreversible.

The compaction model can optionally include disequilibrium, by using the total fluid pressure, when calculating the effective stress. Alternatively the hydrostatic brine pressure is used to calculate the effective stress.

The simulation model also allows for periods of non-deposition and erosional events. The thickness, being deposited and later eroded, is the thickness of the sediments at the surface and not the compacted thickness, which is used for sediments being deposited and not later eroded.

The compressional transit time and the two-way travel time are also calculated based on elastic properties of the minerals, the compressibilities of brine, oil, and gas, and the simulated field of porosity, fluid saturations, and overpressure. According to Wyllie (1976) the sonic transit time of the sediment can be taken as an arithmetic volumetric average. The transit time of the fluid is taken as a geometric volumetric average and the transit time of the rock consisting of randomly distributed minerals is calculated from the average rock density and the geometric volumetric average of the longitudinal modulus, M. In cases where strata are composed of more than one rock type, the transit time is taken as an arithmetic volumetric average of the end members if the strata were deposited as layers and a geometric volumetric average if the strata were deposited in a deltaic environment.

The first principles compaction concept is presented here.